Answer:
a
The student does have enough evidence to refute the college claim
b
The null hypothesis is [tex]H_o : \mu \le 32[/tex]
The alternative hypothesis is [tex]H_a : \mu > 32[/tex]
Step-by-step explanation:
From the question we are told that
The average class size is [tex]\mu = 32[/tex]
The sample size is [tex]n = 40[/tex]
The sample mean is [tex]\= x = 34.8[/tex]
The standard deviation is [tex]\siigma = 99[/tex]
The significance level is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : \mu \le 32[/tex]
The alternative hypothesis is [tex]H_a : \mu > 32[/tex]
Generally the test statistics is mathematically represented as
[tex]z =\frac{\= x - \mu}{ \frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]z = \frac{34.8 - 32}{ \frac{99 }{\sqrt{99} } }[/tex]
=> [tex]z = 0.1789 [/tex]
Generally the p-value is mathematically represented as
[tex]p- value = P (Z > 0.1789)[/tex]
From the z- table
[tex] P (Z > 0.1789) =0.42901 [/tex]
So
[tex]p- value = 0.42901 [/tex]
So from the calculation we can see that [tex]p- value > \alpha[/tex] so we fail to reject the null hypothesis
This means that the student does not have enough evidence to refute the college claim
A rectangular garden is fenced on all sides with 278 feet of fencing. The garden is 9 feet longer than it is
wide. Find the length and width of the garden.
Answer:
Length = 74 feet,
Width = 65 feet
Step-by-step explanation:
If length = l, width = w;
l = 9 + w (Given)
2l + 2w = 278 (Definition of perimeter)
Substitute "9 + w" for l in the second equation;
2(9 + w) + 2w = 278 -> Distribute the "2"
18 + 2w + 2w = 278 -> Combine like terms
18 + 4w = 278 -> Subtract 18 on either side
4w = 260 -> Divide either side by 4
w = 260/4 = 65 feet
l = 9 + 64 = 74 feet
Find the common ratio of the geometric sequence 18,-72,288,...
Answer:
The common ratio of the geometric sequence is -4
Step-by-step explanation:
Geometric Sequence
A geometric sequence is defined as a series of numbers that follow a fixed pattern: Each term equals the previous term times a fixed number called the common ratio. The recursive formula is:
[tex]a_n=a_{n-1}*r[/tex]
Where r is the common ratio.
We are given three terms of a geometric sequence:
18,-72,288,...
To find the common ratio, just divide each term by the previous term:
[tex]\displaystyle r=\frac{-72}{18}=-4[/tex]
Make sure it's a fixed number and test with the third term:
[tex]\displaystyle r=\frac{288}{-72}=-4[/tex]
Since both numbers coincide, the common ratio of the geometric sequence is -4
Find the solution of y=x-3
Answer:
x=3
Step-by-step explanation:
0 = x -3
-x = -3
change the sign to positive so x= 3
A bacteria population increases exponentially at a rate of r% each day. After
32 days, the population has increased by 309%. Find the value of r.
Answer:
r=4.5% daily
Step-by-step explanation:
Exponential Growth
The natural growth of some magnitudes can be modeled by the equation:
[tex]P=P_o(1+r)^t[/tex]
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
We know after t=32 days, the population has increased by 309%. Being the original population P the 100%, then the population reached 309+100= 409%.
Substitute the given values into the model function:
[tex]409\%P_o=100\%P_o(1+r)^{32}[/tex]
Simplifying:
[tex]4.09=(1+r)^{32}[/tex]
We need to solve for r. Taking the 32nd root:
[tex]\sqrt[32]{4.09}=\sqrt[32]{(1+r)^{32}}[/tex]
Simplifying:
[tex]1+r=\sqrt[32]{4.09}=1.045[/tex]
Solving:
[tex]r=1.045-1\Rightarrow r=0.045[/tex]
r=4.5% daily
Explain why each of the following integrals is improper. (a) 4 x x − 3 dx 3 Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral. (b) [infinity] 1 1 + x3 dx 0 Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral. (c) [infinity] x2e−x2 dx −[infinity] Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral. (d) π/4 cot(x) dx 0 Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral.
Answer:
a
Since the integral has an infinite discontinuity, it is a Type 2 improper integral
b
Since the integral has an infinite interval of integration, it is a Type 1 improper integral
c
Since the integral has an infinite interval of integration, it is a Type 1 improper integral
d
Since the integral has an infinite discontinuity, it is a Type 2 improper integral
Step-by-step explanation:
Considering a
[tex]\int\limits^4_3 {\frac{x}{x- 3} } \, dx[/tex]
Looking at this we that at x = 3 this integral will be infinitely discontinuous
Considering b
[tex]\int\limits^{\infty}_0 {\frac{1}{1 + x^3} } \, dx[/tex]
Looking at this integral we see that the interval is between [tex]0 \ and \ \infty[/tex] which means that the integral has an infinite interval of integration , hence it is a Type 1 improper integral
Considering c
[tex]\int\limits^{\infty}_{- \infty} {x^2 e^{-x^2}} \, dx[/tex]
Looking at this integral we see that the interval is between [tex]-\infty \ and \ \infty[/tex] which means that the integral has an infinite interval of integration , hence it is a Type 1 improper integral
Considering d
[tex]\int\limits^{\frac{\pi}{4} }_0 {cot (x)} \, dx[/tex]
Looking at the integral we see that at x = 0 cot (0) will be infinity hence the integral has an infinite discontinuity , so it is a Type 2 improper integral
Find the value of x.
Answer:
20
Step-by-step explanation:
angles on a straight line
(x+20)+7x
open bracket
8x +20 = 180
collect like terms
8x= 180-20
8x=160x
x=160/8
x =20
1.
Solve -x + 9x = -4
Solution x= and x =
Answer:
x = - 1/2Step-by-step explanation:
-x + 9x = -4
8x = -4
x = -4/8
x = -1/2
Three hundred yards of fencing is being used to fence in a rectangular garden. The area of the garden is modeled by a
quadratic function of the rectangle's width, A(w). What does the second coordinate of the vertex of the quadratic function.
A(w), represent?
the minimum width that can be used for the fencing
the maximum area that can be enclosed by the fencing
the width that gives the maximum area
the length that gives the maximum area
Answer:
Opction b)
The maximum area that can be enclosed by the fencing
Step-by-step explanation:
I took the test
The solution is, A(w), represents the maximum area that can be enclosed by the fencing.
Here, we have,
If the width of the garden is w (in yards), then the length of the garden is (150-w) and the area is ...
A(w) = w(150 -w) = -(w² -150w)
A(w) = -(w² -150w +75²) +75²
A(w) = -(w -75)² +5625
In this vertex form, the vertex is (75, 5625).
The graph of area versus width is a parabola that opens downward, so the vertex second coordinate is the maximum area that can be enclosed.
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using the definition of multiplication to explain why a box that is 5 inches high 4 inches wide and 3 inches long has a volume of 5• (3•4) cubic inches explain the parentheses in the expression 5•(3•4)
Given:
Height of box = 5 inches
Breadth (width) of box = 4 inches
Length of box = 3 inches
Volume of box = 5 • (3 • 4) cubic inches
To find:
The explanation for the parentheses in the expression 5•(3•4)
Solution:
We know that,
Volume of a box is
[tex]Volume = length \times breadth \times height[/tex]
Area of a rectangle is
[tex]Area = length \times width[/tex]
Now,
Volume of box = 5 • (3 • 4) cubic inches
In this expression, (3 • 4) represents the product of length and with of the box. So, it means represents area of the base of box and after multiplying the base area with height we get the volume of the box.
Therefore, the parentheses in the expression 5•(3•4) represents the base area of the box.
what is 2208 divided by 96?
23............hope this helps
Which equation represents a line that passes through (2,-1/2) and has a slope of 3?
y - 2 = 3(x + 1/2)
y - 3 = 2(x + 1/2)
y + 1/2 = 3(x - 2)
y + 1/2 = 2(x - 3)
Solve for the value of Q
Answer:
q=9
Step-by-step explanation:
5q+1+44=90
5q+45=90
5q=45
q=9
(2/5) (-5/7) please show work
(2/5) (-5/7)
What we have to do?To simplify the equation
Step by step explanation:Step 1:
[tex] \blue{= \dfrac{2}{5} \times \dfrac{ - 5}{7} }[/tex]
[tex]\green{so \: after \: simplifying \: the \: equation \: it \: will \: look \: like \: this}[/tex]
Step 2:
[tex] \blue{= \dfrac{2}{1} \times \dfrac{ - 1}{7} }[/tex]
Step 3:
[tex] \blue{=\dfrac{ - 2}{7} }[/tex]
Step 4:
[tex]\blue{=−0.28571✓}[/tex]
________________________________With regards!
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The graph models the heights, in feet, of two objects dropped from different heights after x seconds.
On a coordinate plane, y = f (x) curves down through (0, 35) and (1, 20). G (x) curves down through (0, 30) and (0.5, 25).
Which equation represents g(x) as a transformation of f(x)?
g(x) = f(x) – 5
g(x) = f(x – 5)
g(x) = f(x) + 5
g(x) = f(x + 5)
Answer:
g(x) = f(x) + 5
Step-by-step explanation:
C
Answer: g(x) = f(x) - 5
Step-by-step explanation:
y = mx + b
The Graph of g(x) is 5 units down from the graph of f(x)
Help!!
...................................................................................
What is the perimeter of the rectangle?
5 feet
6 feet
12 feet
X 36 feet
Answer: I think the answer is b
Step-by-step explanation:
The frequency distribution chart below represents scores from a math quiz. A histogram titled frequency has score on the x-axis and frequency on the y-axis. 65 to 70 is 1, 71 to 76 is 1, 77 to 82 is 1, 83 to 88 is 3, 89 to 94 is 4, 95 to 100 is 2. Which statement best describes the data? a. The data is skewed left. c. The data is skewed right. b. The data is symmetric. d. There is no pattern to the data.
Answer:
a. the data is skewed to the left
Step-by-step explanation:
on the left most of the data is lower than the data on the right + i took the quiz
Answer:
A
Step-by-step explanation:
Which two ratios show a proportional relationship?
A. 2/8 and 6/20
B. 4/6 and 15/20
C. 10/15 and 12/18
D. 15/18 and 20/25
The perimeter of a rectangular solar panel is 540 cm. The ratio of the length to the width is 3 : 2. What are the length and width?
Total number of parts = 3 + 2 = 5 parts
[tex]each \: part \: = \frac{(540 \div 5)}{2} \: m[/tex]
[tex] \\ each \: part \: = \frac{108}{2} m \: \\ \\ each \: part \: = 54 \: m[/tex]
Then , the length of this triangle :
[tex]54 \times 3 \: m[/tex]
[tex] = 162 \: m[/tex]
Then , the width of this triangle will be :
[tex]54 \times 2 \: m[/tex]
[tex]108 \: m[/tex]
∴ The length of this rectangle is 162 m and the width of this rectangle is 108 m .
3. Which list contains all of the factors of the number 48?
(1 point)
1, 2, 3, 4, 6, 8, 12, 16, 24
2, 3, 4, 6, 8, 12, 16, 24, 48
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
1, 2, 3, 4, 6, 8, 9, 12, 16, 24, 48
Answer:
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
so the 3rd option is correct
Answer:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
C
Step-by-step explanation:
got it right on test
Five notebooks cost $20 at this rate how much would 4 notebooks coat?
Answer:
$16
Step-by-step explanation:
if 5=20 then 20÷5=4 and 4x4=16
Answer:
16
Step-by-step explanation:
$20/5notebooks=$4 each
4$*4notebooks=16$
PLEASE HELP 50 PTS
For a function j(x), the difference quotient is 3x2 + 3xh + h2. What is the average rate of change of j(x) over the interval [–1, 6]?
15
21
25
31
Answer:
31 is correct guys
Step-by-step explanation:
Since the data is incomplete, for the given question the required average rate of change is given by 15 + 3h.
Given that,
For a function j(x), the difference quotient is 3x2 + 3xh + h2.
The average rate of change of j(x) over the interval [–1, 6] is to be determined.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is independent while Y is the dependent variable.
Here, the average rate of change = f(6) - f(-1) / (6 + 1)
So,
f(6) = 108 + 18h + h²
f(-1) = 3 - 3h + h²
Now,
average rate of change = [(108 + 18h + h²) - (3 - 3h + h²)]/(7)
= [105 + 21 h ] / 7
= 15 + 3h
Thus, the required average rate of change is given by 15 + 3h.
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How many grams in one dose of medicine?
Answer:
65
Step-by-step explanation:
Find the difference: 34.14 - 67.42
Answer:
the answer is -33.28
Step-by-step explanation:
Write an equation for the description.
Tanmayi wants to raise $150 for a school fundraiser. She has raised $100 so far. How much more (bes she
need to reach her goal? Let m be how much more is needed.
Answer:
answer
Step-by-step explanation:
step by step explanation
What is the cardinal number of the set containing all negative integers greater than −8?
Answer: positive 7
Step-by-step explanation:
Cardinal number of the set containing all negative integers greater than −8 is 7.
What are cardinal number?In mathematics,cardinal numbers or cardinals for short, are generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number: the number of elements in the set.
Now the given set is all negative integers greater than -8.
Let S be the set,so
S = {-7,-6,-5,-4,-3,-2,-1}
now to find the cardinality, we see that set S has 7 elements.
Cardinality of Set S is 7.
Hence, cardinal number of the set containing all negative integers greater than −8 is 7.
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QUESTION 1 OF 5
4c + 5 < 4c + 3
Which of the follow
Answer: No solutions.
============================================
Work Shown:
4c + 5 < 4c + 3
4c+5-4c < 4c+3-4c ... subtract 4c from both sides
4c-4c+5 < 4c-4c+3
0c+5 < 0c+3
0+5 < 0+3
5 < 3 ... statement is false
Since that statement is false, this means the original inequality is false regardless of what you pick for c.
There are no solutions.
m
/
n
(x), x not equal to
Answer:
In M/n(x) x cannot be 0
Step-by-step explanation:
If any number is divided by 0, then that number is undefined and has no answer, so in math this is always avoided by not dividing with 0.
Fill in the missing term on each line. Simplify any fractions.
8(d + 1) = 8
d + 1 =
Divide both sides by 8
d =
Subtract 1 from both sides
Answer:
8 subtract 1 sides fraction
Answer:
8 subtract 1 sides fraction
Step-by-step explanation:
Which of the following is the value or PQ
Answer:
B. 61
Step-by-step explanation:
Given:
∆PQR ≅ ∆PQS
PQ = 2x + 41
QS = 7x - 24
QR = 3x + 16
Required:
Numerical value of PQ
SOLUTION:
First, create an equation to find the value of x as follows:
Since both triangles are congruent, therefore:
QS = QR
7x - 24 = 3x + 16 (Substitution)
Collect like terms
7x - 3x = 24 + 16
4x = 40
Divide both sides by 4
4x/4 = 40/4
x = 10
Find PQ by plugging x = 10 into PQ = 2x + 41
PQ = 2(10) + 41
PQ = 20 + 41
PQ = 61
